Triangles Diagonal Bell

Regular linear triangles having the Bell numbers in a column or a diagonal

A011971 0 FC Aitken's array: triangle of numbers {a(n,k), n >= 0, 0<=k<=n} read by rows, defined by a(0,0)=1, a(n,0)=a(n-1,n-1), a(n,k)=a(n,k-1)+a(n-1,k-1).

A011971 0 LD Aitken's array: triangle of numbers {a(n,k), n >= 0, 0<=k<=n} read by rows, defined by a(0,0)=1, a(n,0)=a(n-1,n-1), a(n,k)=a(n,k-1)+a(n-1,k-1).

A011972 0 FC Sequence formed by reading rows of triangle defined in A011971.

A033306 0 FC Triangle of coefficients of ordered cycle-index polynomials: T(n,k) = binomial(n,k)*Bell(k)*Bell(n-k).

A033306 0 LD Triangle of coefficients of ordered cycle-index polynomials: T(n,k) = binomial(n,k)*Bell(k)*Bell(n-k).

A035347 0 LD Triangle of a(n,k) = number of minimal covers of an n-set that cover k points of that set uniquely (n >= 1, k >= 1).

A036073 0 FC Triangle of coefficients arising in calculation of A002875 (sorting numbers).

A039810 0 FC Matrix square of Stirling-2 Triangle A008277: 2-levels set partitions of [n] into k first-level subsets.

A046817 0 LD Triangle of generalized Stirling numbers of 2nd kind.

A049020 0 FC Triangle of numbers a(n,k), 0<=k<=n, related to Bell numbers.

A055883 0 FC Exponential transform of Pascal's triangle A007318.

A055883 0 LD Exponential transform of Pascal's triangle A007318.

A055896 0 LD Exponential transform of Stirling-2 triangle A008277.

A055924 0 LD Exponential transform of Stirling-1 triangle A008275.

A056857 0 FC Triangle read by rows: T(n,c) = number of successive equalities in set partitions of n.

A056860 0 LD Triangle T(n,k) = number of element-subset partitions of {1..n} with n-k+1 equalities (n >= 1, 1<=k<=n).

A059098 0 FC Triangle T(n,m) = Sum_{i=0..n} stirling2(n,i)*Product_{j=1..m} (i-j+1), m=0..n.

A059340 0 FC Triangle T(n,k) of numbers with e.g.f. exp((exp((1+x)*y)-1)/(1+x)), k=0..n-1.

A066045 0 LD Triangle T(n,k) defined by Sum_{1<=k<=n} T(n,k)*u^k*t^n/n! = exp((1-t)*(1-t^2)*(1-t^3)...)^(-u)-1).

A079005 0 LD Exponential transform of unsigned Lah-triangle |A008297(n,k)|.

A085838 0 LD Triangle T(n,k) read by rows; given by [0,1,0,1,0,1,0,1,...] DELTA [1,1,1,2,1,3,1,4,1,5,1,6,...], where DELTA is Deléham's operator defined in A084938.

A090210 0 FC Triangle of certain generalized Bell numbers.

A093936 0 LD Table T(n,k) read by rows which contains in row n and column k the sum of A001055(A036035(n,j)) over all column indices j where A036035(n,j) has k distinct prime factors.

A095149 0 FC Triangle read by rows: Aitken's array (A011971) but with a leading diagonal before it given by the Bell numbers (A000110), 1, 1, 2, 5, 15, 52, ...

A095149 0 LD Triangle read by rows: Aitken's array (A011971) but with a leading diagonal before it given by the Bell numbers (A000110), 1, 1, 2, 5, 15, 52, ...

A095149 0 SC Triangle read by rows: Aitken's array (A011971) but with a leading diagonal before it given by the Bell numbers (A000110), 1, 1, 2, 5, 15, 52, ...

A095674 0 FC Triangle read by rows, formed from product of Pascal's triangle (A007318) and Aitken's (or Bell's) triangle (A011971).

A095674 0 LD Triangle read by rows, formed from product of Pascal's triangle (A007318) and Aitken's (or Bell's) triangle (A011971).

A095675 0 LD Triangle read by rows, formed from product of Aitken's (or Bell's) triangle (A011971) and Pascal's triangle (A007318).

A102661 0 LD Triangle of partial sums of Stirling numbers of 2nd kind (A008277): T(n,k) = Sum_{i=1..k} Stirling2(n,i), 1<=k<=n.

A106436 0 LD Difference array of Bell numbers A000110 read by antidiagonals.

A106436 0 SC Difference array of Bell numbers A000110 read by antidiagonals.

A108087 0 FC Array, read by antidiagonals, where A(n,k) = exp(-1)*Sum_{i>=0}(i+k)^n/i!.

A108087 0 SC Array, read by antidiagonals, where A(n,k) = exp(-1)*Sum_{i>=0}(i+k)^n/i!.

A108458 0 LD Triangle read by rows: T(n,k) is the number of set partitions of {1,2,...,n} in which the last block is the singleton {k}, 1<=k<=n; the blocks are ordered with increasing least elements.

A111673 0 SC Triangle, generated from A111579.

A113547 0 LD Triangle read by rows: number of labeled partitions of n with maximin m.

A113547 0 SD Triangle read by rows: number of labeled partitions of n with maximin m.

A118984 0 FC Triangular T(n,k) which contains in column k>=0 the elements of the Stirling transform of the unsigned sequence Stirling1(j+k,j), j>=0.

A120057 0 FC Table T(n,k) = sum over all set partitions of n of number at index k.

A121207 0 LD Triangle read by rows. The definition is by diagonals. The r-th diagonal from the right, for r >= 0, is given by b(0) = b(1) = 1; b(n+1) = Sum_{k=0..n} binomial(n+2,k+r)*a(k).

A123081 0 FC Infinite square array read by antidiagonals: T(n,k) = Bell(n+k) = A000110(n+k), n >= 0, k >= 0.

A123081 0 LD Infinite square array read by antidiagonals: T(n,k) = Bell(n+k) = A000110(n+k), n >= 0, k >= 0.

A123081 0 SC Infinite square array read by antidiagonals: T(n,k) = Bell(n+k) = A000110(n+k), n >= 0, k >= 0.

A123081 0 SD Infinite square array read by antidiagonals: T(n,k) = Bell(n+k) = A000110(n+k), n >= 0, k >= 0.

A123158 0 FC Square array related to Bell numbers read by antidiagonals.

A123158 0 SC Square array related to Bell numbers read by antidiagonals.

A123346 0 FC Mirror image of the Bell triangle A011971, which is also called the Pierce triangle or Aitken's array.

A123346 0 LD Mirror image of the Bell triangle A011971, which is also called the Pierce triangle or Aitken's array.

A125178 0 FC Triangle read by rows: T(n,0)=B(n) (the Bell numbers, A000110(n)), T(n,k)=0 for k<0 or k>n, T(n,k)=T(n-1,k)+T(n-1,k-1) for n>=1, 0<=k<=n.

A125311 1 SD Array giving number of (k,2)-noncrossing partitions of n, read by antidiagonals.

A126350 0 LD Triangle read by rows: matrix product of the binomial coefficients with the Stirling numbers of the second kind.

A126442 0 LD Triangular array t read by rows: t(0,k) is p(k), the number of partitions of the k-multiset {0,0,...,0} with k zeros. For 0 <= n < k, t(n, k) is the number of partitions of the k-multiset {0, 0, ..., 0, 1, 2, 3, ..., k-n} with n zeros.

A127568 0 LD Triangle T(n,k) = Bell(k) = A000110(k), 0<=k<=n.

A127568 0 SD Triangle T(n,k) = Bell(k) = A000110(k), 0<=k<=n.

A130191 0 SC Square of the Stirling2 matrix A048993.

A133611 0 FC A triangular array of numbers related to factorization and number of parts in Murasaki diagrams.

A133611 0 SC A triangular array of numbers related to factorization and number of parts in Murasaki diagrams.

A136789 0 LD Triangle read by rows: A007318^(-1) * A011971.

A136790 0 LD Triangle read by rows: A011971 * A007318^(-1).

A137597 0 FC Triangle read by rows: A008277 * A007318.

A137650 0 FC Triangle read by rows, A008277 * A000012.

A143396 0 LD Triangle T(n,k) = number of forests of labeled rooted trees of height at most 1, with n labels, k of which are used for root nodes and any root may contain >= 1 labels, n >= 0, 0<=k<=n.

A143983 0 FC Triangle T(n,k), n>=1, 1<=k<=n, read by rows, where sequence a_k of column k has a_k(0)=1, followed by (k-1)-fold 0 and a_k(n) shifts k places down under binomial transform.

A144150 0 SD Square array A(n,k), n>=0, k>=0, read by antidiagonals, where the e.g.f. of column k is 1+g^(k+1)(x) with g = x-> exp(x)-1.

A144155 0 FC Bell convolution triangle, T(n,k) = A000110(n-k)*A000110(k)

A144155 0 LD Bell convolution triangle, T(n,k) = A000110(n-k)*A000110(k)

A144155 0 SC Bell convolution triangle, T(n,k) = A000110(n-k)*A000110(k)

A144155 0 SD Bell convolution triangle, T(n,k) = A000110(n-k)*A000110(k)

A145460 0 LD Square array A(n,k), n>=0, k>=0, read by antidiagonals, where sequence a_k of column k is the exponential transform of C(n,k).

A152431 0 LD Eigentriangle, row sums = A000110, the Bell numbers.

A152431 0 SD Eigentriangle, row sums = A000110, the Bell numbers.

A152432 0 LD Triangle read by rows, inverse binomial transform of A152431.

A152433 0 LD Triangle read by rows, A000012^(-1) * A152431

A153277 0 LD Array read by antidiagonals of higher order Bell numbers.

A154380 0 FC Triangle T(n,k), 0<=k<=n, read by rows given by [1, 1, 1, 2, 1, 3, 1,4,1,...] DELTA [1, 0, 0,0,...] where DELTA is the operator defined in A084938.

A160185 0 FC Triangle read by rows, (1 / ((-1)*A129184 * A007318 + I)) - I, I = Identity matrix.

A162663 0 LD Table by antidiagonals, T(n,k) is the number of partitions of {1..(nk)} that are invariant under a permutation consisting of n k-cycles.

A167128 0 LD Triangle T(m,n) read by rows: T(m,n) = Sum_{k=1..n} StirlingS2(m, n) * StirlingS2(m, k).

A171840 0 LD Triangle read by rows, truncated columns of an array formed by taking sets of P(n) = Pascal's triangle, with the 1's column shifted up n = 1,2,3,...times. Then n-th row of the array = Lim_{k->inf.}, k=1,2,3,...; (P(n))^k, deleting the first 1.

A182930 0 FC Triangle read by rows: Number of set partitions of {1,2,..,n} such that |k| is a block and no block |m| with m < k exists, (1 <= n, 1 <= k <= n).

A182930 0 SD Triangle read by rows: Number of set partitions of {1,2,..,n} such that |k| is a block and no block |m| with m < k exists, (1 <= n, 1 <= k <= n).

A182931 0 FC Generalized Bell numbers; square array read by diagonals.

A182933 0 SC Generalized Bell numbers based on the rising factorial powers; square array read by antidiagonals.

A186020 0 FC Eigentriangle of the binomial matrix.

A188392 0 FC T(n,k) = number of (n*k) X k binary arrays with rows in nonincreasing order and n ones in every column.

A188445 0 FC T(n,k)=Number of (n*k)Xk binary arrays with nonzero rows in decreasing order and n ones in every column

A188792 0 LD Table with T(n,k) the number of word structures of length n which can be decomposed into k palindromes but not fewer.

A189233 0 SC Square array A(n,k), n >= 0, k >= 0, read by diagonals, where the e.g.f. of column k is exp(k*(e^x-1)).

A198914 0 FC T(n,k)=Number of nXk 0..7 arrays with values 0..7 introduced in row major order and no element equal to any horizontal or vertical neighbor

A198914 0 LD T(n,k)=Number of nXk 0..7 arrays with values 0..7 introduced in row major order and no element equal to any horizontal or vertical neighbor

A205574 0 SC Triangle T(n,k), 0<=k<=n, given by (0, 1, 1, 1, 2, 1, 3, 1, 4, 1, 5, 1, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.

A206503 0 FC T(n,k)=Number of nXk 0..7 arrays with no element equal to another within a city block distance of two, and new values 0..7 introduced in row major order

A206503 0 LD T(n,k)=Number of nXk 0..7 arrays with no element equal to another within a city block distance of two, and new values 0..7 introduced in row major order

A207868 0 FC T(n,k)=Number of nXk nonnegative integer arrays with new values 0 upwards introduced in row major order and no element equal to any horizontal or vertical neighbor (colorings ignoring permutations of colors)

A207868 0 LD T(n,k)=Number of nXk nonnegative integer arrays with new values 0 upwards introduced in row major order and no element equal to any horizontal or vertical neighbor (colorings ignoring permutations of colors)

A207981 0 FC T(n,k)=Number of nXk nonnegative integer arrays with new values 0 upwards introduced in row major order and no element equal to any diagonal or antidiagonal neighbor (colorings ignoring permutations of colors)

A207981 0 LD T(n,k)=Number of nXk nonnegative integer arrays with new values 0 upwards introduced in row major order and no element equal to any diagonal or antidiagonal neighbor (colorings ignoring permutations of colors)

A208001 0 FC T(n,k)=Number of nXk nonnegative integer arrays with new values 0 upwards introduced in row major order and no element equal to any knight-move neighbor (colorings ignoring permutations of colors)

A208001 0 LD T(n,k)=Number of nXk nonnegative integer arrays with new values 0 upwards introduced in row major order and no element equal to any knight-move neighbor (colorings ignoring permutations of colors)

A208021 0 FC T(n,k)=Number of nXk nonnegative integer arrays with new values 0 upwards introduced in row major order and no element equal to any horizontal, vertical, diagonal or antidiagonal neighbor (colorings ignoring permutations of colors)

A208021 0 LD T(n,k)=Number of nXk nonnegative integer arrays with new values 0 upwards introduced in row major order and no element equal to any horizontal, vertical, diagonal or antidiagonal neighbor (colorings ignoring permutations of colors)

A208054 0 FC T(n,k)=Number of nXk nonnegative integer arrays with new values 0 upwards introduced in row major order and no element equal to any horizontal, vertical or antidiagonal neighbor (colorings ignoring permutations of colors)

A208054 0 LD T(n,k)=Number of nXk nonnegative integer arrays with new values 0 upwards introduced in row major order and no element equal to any horizontal, vertical or antidiagonal neighbor (colorings ignoring permutations of colors)

A208096 0 FC T(n,k)=Number of nXk nonnegative integer arrays with new values 0 upwards introduced in row major order and no element equal to any horizontal, diagonal or antidiagonal neighbor (colorings ignoring permutations of colors)

A208096 0 LD T(n,k)=Number of nXk nonnegative integer arrays with new values 0 upwards introduced in row major order and no element equal to any horizontal, diagonal or antidiagonal neighbor (colorings ignoring permutations of colors)

A208301 0 FC T(n,k)=Number of nXk nonnegative integer arrays with new values 0 upwards introduced in row major order and no element equal to any horizontal or antidiagonal neighbor (colorings ignoring permutations of colors)

A208301 0 LD T(n,k)=Number of nXk nonnegative integer arrays with new values 0 upwards introduced in row major order and no element equal to any horizontal or antidiagonal neighbor (colorings ignoring permutations of colors)

A208466 0 FC T(n,k)=Number of nXk nonnegative integer arrays with new values 0 upwards introduced in row major order and no element equal to more than two of its immediate leftward or upward or right-upward antidiagonal neighbors

A208466 0 LD T(n,k)=Number of nXk nonnegative integer arrays with new values 0 upwards introduced in row major order and no element equal to more than two of its immediate leftward or upward or right-upward antidiagonal neighbors

A208581 0 FC T(n,k)=Number of nXk nonnegative integer arrays with new values 0 upwards introduced in row major order and no element equal to more than one of its immediate leftward or upward or right-upward antidiagonal neighbors

A208581 0 LD T(n,k)=Number of nXk nonnegative integer arrays with new values 0 upwards introduced in row major order and no element equal to more than one of its immediate leftward or upward or right-upward antidiagonal neighbors

A208788 0 FC T(n,k)=Number of nXk nonnegative integer arrays with new values 0 upwards introduced in row major order and no element equal to any antidiagonal neighbor (colorings ignoring permutations of colors)

A208788 0 LD T(n,k)=Number of nXk nonnegative integer arrays with new values 0 upwards introduced in row major order and no element equal to any antidiagonal neighbor (colorings ignoring permutations of colors)

A209527 0 FC T(n,k)=Number of nXk 0..7 arrays with every 2X2 subblock containing exactly one value repeat, and new values 0..7 introduced in row major order

A209527 0 LD T(n,k)=Number of nXk 0..7 arrays with every 2X2 subblock containing exactly one value repeat, and new values 0..7 introduced in row major order

A210545 0 LD T(n,k)=Number of arrays of n nonnegative integers with value i>0 appearing only after i-1 has appeared at least k times

A211561 0 LD T(n,k) = number of nonnegative integer arrays of length n+k-1 with new values 0 upwards introduced in order, and containing the value k-1.

A211700 0 LD T(n,k)=Number of nonnegative integer arrays of length n+2k-2 with new values introduced in order 0 upwards and every value appearing only in runs of at least k

A212431 0 FC Triangle read by rows: row sums, right and left borders are the Bell sequence, or a shifted variant. See Comments for precise definition.

A212431 0 LD Triangle read by rows: row sums, right and left borders are the Bell sequence, or a shifted variant. See Comments for precise definition.

A212431 0 SD Triangle read by rows: row sums, right and left borders are the Bell sequence, or a shifted variant. See Comments for precise definition.

A215745 0 SC T(n,k)=Number of horizontal, vertical, diagonal and antidiagonal neighbor colorings of the odd squares of an nXk array with new integer colors introduced in row major order

A215745 0 SD T(n,k)=Number of horizontal, vertical, diagonal and antidiagonal neighbor colorings of the odd squares of an nXk array with new integer colors introduced in row major order

A215847 0 SC T(n,k)=Number of horizontal, vertical, diagonal and antidiagonal neighbor colorings of the even squares of an nXk array with new integer colors introduced in row major order

A215847 0 SD T(n,k)=Number of horizontal, vertical, diagonal and antidiagonal neighbor colorings of the even squares of an nXk array with new integer colors introduced in row major order

A215904 0 SC T(n,k)=Number of diagonal and antidiagonal neighbor colorings of the even squares of an nXk array with new integer colors introduced in row major order

A215904 0 SD T(n,k)=Number of diagonal and antidiagonal neighbor colorings of the even squares of an nXk array with new integer colors introduced in row major order

A215924 0 SC T(n,k)=Number of diagonal and antidiagonal neighbor colorings of the odd squares of an nXk array with new integer colors introduced in row major order

A215924 0 SD T(n,k)=Number of diagonal and antidiagonal neighbor colorings of the odd squares of an nXk array with new integer colors introduced in row major order

A216460 0 SC T(n,k)=Number of horizontal, diagonal and antidiagonal neighbor colorings of the even squares of an nXk array with new integer colors introduced in row major order

A216460 0 SD T(n,k)=Number of horizontal, diagonal and antidiagonal neighbor colorings of the even squares of an nXk array with new integer colors introduced in row major order

A216612 0 SC T(n,k)=Number of horizontal, diagonal and antidiagonal neighbor colorings of the odd squares of an nXk array with new integer colors introduced in row major order

A216612 0 SD T(n,k)=Number of horizontal, diagonal and antidiagonal neighbor colorings of the odd squares of an nXk array with new integer colors introduced in row major order

A216663 0 FC T(n,k)=Number of horizontal, vertical or knight-move neighbor colorings of an nXk array with new integer colors introduced in row major order

A216663 0 LD T(n,k)=Number of horizontal, vertical or knight-move neighbor colorings of an nXk array with new integer colors introduced in row major order

A216694 0 FC T(n,k)=Number of horizontal, vertical, diagonal or knight-move neighbor colorings of an nXk array with new integer colors introduced in row major order

A216694 0 LD T(n,k)=Number of horizontal, vertical, diagonal or knight-move neighbor colorings of an nXk array with new integer colors introduced in row major order

A216760 0 FC T(n,k)=Number of horizontal, vertical, diagonal, antidiagonal or knight-move neighbor colorings of an nXk array with new integer colors introduced in row major order

A216760 0 LD T(n,k)=Number of horizontal, vertical, diagonal, antidiagonal or knight-move neighbor colorings of an nXk array with new integer colors introduced in row major order

A217204 0 FC Triangle read by rows, related to Bell numbers A000110.

A219585 0 SC Number A(n,k) of k-partite partitions of (n)^k into distinct k-tuples; square array A(n,k), n>=0, k>=0, read by antidiagonals.

A219727 0 SC Number A(n,k) of k-partite partitions of (n)^k into k-tuples; square array A(n,k), n>=0, k>=0, read by antidiagonals.

A229223 0 LD Number G(n,k) of set partitions of {1,...,n} into sets of size at most k; triangle G(n,k), n>=0, 0<=k<=n, read by rows.

A229243 0 SD Number A(n,k) of set partitions of {1,...,k*n} into sets of size at most n; square array A(n,k), n>=0, k>=0, read by antidiagonals.

A233357 0 FC Triangle read by rows: T(n,k) = ((Stirling2)^2)(n,k) * k!

A241578 0 SD Square array read by anti-diagonals upwards: T(n,k) = Sum_{j=1..k} n^(k-j)*Stirling_2(k,j) (n >= 0, k >= 1).

A241579 0 SC Square array read by anti-diagonals downwards: T(n,k) = Sum_{j=1..k} n^(k-j)*Stirling_2(k,j) (n >= 0, k >= 1).

A244489 0 FC Triangle read by rows: T(n,k) = Sum_{j=k..n} binomial(n,j)*Stirling_2(j,k)*Bell(n-j), where Bell(n) = A000110(n), for n >= 1, 0 <= k <= n-1.

A255903 0 LD Number T(n,k) of collections of nonempty multisets with a total of n objects of exactly k colors; triangle T(n,k), n>=0, 0<=k<=n, read by rows.

A256550 0 SC Triangle read by rows, T(n,k) = EL(n,k)/(n-k+1)! and EL(n,k) the matrix-exponential of the unsigned Lah numbers scaled by exp(-1), for n>=0 and 0<=k<=n.

A259691 0 FC Triangle read by rows, another version of A056857.

A259697 0 LD Triangle read by rows: T(n,k) = number of rook patterns on n X n board where bottom rook is in column k.

A259697 0 SD Triangle read by rows: T(n,k) = number of rook patterns on n X n board where bottom rook is in column k.

A260876 0 SD Square array read by ascending antidiagonals: number of m-shape set partitions.

A264428 0 SC Triangle read by rows, Bell transform of Bell numbers.

A265312 0 SD Square array read by ascending antidiagonals, Bell numbers iterated by the Bell transform.

A270701 0 FC Total sum T(n,k) of the sizes of all blocks with maximal element k in all set partitions of {1,2,...,n}; triangle T(n,k), n>=1, 1<=k<=n, read by rows.

A270702 0 LD Total sum T(n,k) of the sizes of all blocks with minimal element k in all set partitions of {1,2,...,n}; triangle T(n,k), n>=1, 1<=k<=n, read by rows.

A274835 0 SD Number A(n,k) of set partitions of [n] such that the difference between each element and its block index is a multiple of k; square array A(n,k), n>=0, k>=0, read by antidiagonals.

A274859 0 SD Number A(n,k) of set partitions of [n] such that the difference between each element and its index (in the partition) is a multiple of k; square array A(n,k), n>=0, k>=0, read by antidiagonals.

A275043 0 SD Number A(n,k) of set partitions of [k*n] such that within each block the numbers of elements from all residue classes modulo k are equal for k>0, A(n,0)=1; square array A(n,k), n>=0, k>=0, read by antidiagonals.

A275069 0 SD Number A(n,k) of set partitions of [n] such that i-j is a multiple of k for all i,j belonging to the same block; square array A(n,k), n>=0, k>=0, read by antidiagonals.

different prefixes

A007723 2 SD Triangle a(n,k) of number of M-sequences read by antidiagonals. {0, 2, 1, 2, 5, 15, 52, 203, 877, 4140}

possible typos

A111672 0 SD Array T(n,k) = A153277(n-1,k) = A144150(n,k) read downwards antidiagonals. {1, 2, 5, 15, 52, 203, 877, 21147}

near misses, look-alikes, variations, coincidences

Bell numbers

1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, 678570, 4213597, 27644437, 190899322, 1382958545

A002134 0 SC Generalized divisor function. Partitions of n using only 3 types of piles. {5, 15, 52, 154, 385, 910, 1938, 3703}

A003413 0 SD From a nim-like game. {2, 5, 15, 52, 233, 1351, 10060, 96239}

A008631 0 SC Molien series for alternating group Alt_8 (or A_8). {2, 5, 15, 52, 186, 638, 2105, 6659}

A008637 0 SC Number of partitions of n into at most 8 parts. {2, 5, 15, 52, 186, 638, 2104, 6630}

A023028 0 SC Number of partitions of n into 8 unordered relatively prime parts. {2, 5, 15, 52, 180, 621, 2104, 6614}

A035977 0 FC Number of partitions of n into parts not of the form 19k, 19k+8 or 19k-8. Also number of partitions with at most 7 parts of size 1 and differences between parts at distance 8 are greater than 1. {1, 2, 5, 15, 52, 202, 811, 3388, 14638}

A036803 0 SC Number of partitions satisfying (cn(1,5) <= cn(2,5) and cn(1,5) <= cn(3,5) and cn(4,5) <= cn(2,5) and cn(4,5) <= cn(3,5)). {1, 2, 5, 15, 52, 207, 909, 3997}

A077866 0 SC Expansion of (1-x)^(-1)/(1-x-2*x^2+2*x^3). {5, 15, 52, 240, 1515, 12261, 131038}

A089958 0 SD Number of partitions of n in which every part occurs 2, 3, or 5 times. {0, 1, 3, 5, 15, 52, 136, 368, 1088}

A098491 0 FC Number of partitions of n with parts occurring at most thrice and an even number of parts. Row sums of A098489. {1, 0, 1, 5, 15, 52, 197, 770, 3082}

A098887 0 SC Number of nonisomorphic groups with orders indexed by least prime signatures. {2, 5, 15, 52, 47, 177, 775, 150}

A137855 3 SD Triangle read by rows, antidiagonals of the array A000012 * A008277(transform). {0, 1, 1, 1, 2, 5, 15, 52, 202, 855}

A160571 0 SC G.f.: Product_{n>=1} (1 + x^n + x^(n+1)). {2, 5, 15, 52, 200, 819, 3507, 15496}

A198528 0 FC T(n,k)=Number of nXk 0..4 arrays with values 0..4 introduced in row major order and each element equal to no more than two horizontal and vertical neighbors {1, 2, 5, 15, 52, 202, 855}

A198528 0 LD T(n,k)=Number of nXk 0..4 arrays with values 0..4 introduced in row major order and each element equal to no more than two horizontal and vertical neighbors {1, 2, 5, 15, 52, 202, 855}

A198723 0 FC T(n,k)=Number of nXk 0..6 arrays with values 0..6 introduced in row major order and no element equal to any horizontal or vertical neighbor {1, 1, 2, 5, 15, 52, 203, 876}

A198723 0 LD T(n,k)=Number of nXk 0..6 arrays with values 0..6 introduced in row major order and no element equal to any horizontal or vertical neighbor {1, 1, 2, 5, 15, 52, 203, 876}

A198982 0 FC T(n,k)=Number of nXk 0..5 arrays with values 0..5 introduced in row major order and no element equal to any horizontal or vertical neighbor {1, 1, 2, 5, 15, 52, 202, 855}

A198982 0 LD T(n,k)=Number of nXk 0..5 arrays with values 0..5 introduced in row major order and no element equal to any horizontal or vertical neighbor {1, 1, 2, 5, 15, 52, 202, 855}

A203647 2 SD T(n,k) = number of arrays of n 0..k integers with new values introduced in order 0..k but otherwise unconstrained. Array read by antidiagonals. {0, 2, 1, 2, 5, 15, 52, 202, 855, 3845}

A206389 0 FC T(n,k)=Number of nXk 0..6 arrays with no element equal to another within a city block distance of two, and new values 0..6 introduced in row major order {1, 1, 1, 2, 5, 15, 52, 202, 855}

A206389 0 LD T(n,k)=Number of nXk 0..6 arrays with no element equal to another within a city block distance of two, and new values 0..6 introduced in row major order {1, 1, 1, 2, 5, 15, 52, 202, 855}

A209465 0 FC T(n,k)=Number of nXk 0..6 arrays with every 2X2 subblock containing exactly one value repeat, and new values 0..6 introduced in row major order {1, 2, 5, 15, 52, 203, 877, 4139}

A209465 0 LD T(n,k)=Number of nXk 0..6 arrays with every 2X2 subblock containing exactly one value repeat, and new values 0..6 introduced in row major order {1, 2, 5, 15, 52, 203, 877, 4139}

A209503 0 FC T(n,k)=Number of nXk 0..4 arrays with every 2X2 subblock containing exactly one value repeat, and new values 0..4 introduced in row major order {1, 2, 5, 15, 52, 202, 855, 3845}

A209503 0 LD T(n,k)=Number of nXk 0..4 arrays with every 2X2 subblock containing exactly one value repeat, and new values 0..4 introduced in row major order {1, 2, 5, 15, 52, 202, 855, 3845}

A209744 0 FC T(n,k)=Number of nXk 0..5 arrays with every 2X2 subblock containing exactly one value repeat, and new values 0..5 introduced in row major order {1, 2, 5, 15, 52, 203, 876, 4111}

A209744 0 LD T(n,k)=Number of nXk 0..5 arrays with every 2X2 subblock containing exactly one value repeat, and new values 0..5 introduced in row major order {1, 2, 5, 15, 52, 203, 876, 4111}

A238866 0 SC Number of partitions of n where the difference between consecutive parts is at most 6. {2, 5, 15, 52, 202, 810, 3401, 14818, 66190}

A239469 0 SD Number of 3-separable partitions of n; see Comments. {0, 2, 5, 15, 52, 177, 630, 2345, 9087}

A240671 0 SD Floor(4^n/(2+2*cos(2*Pi/7))^n). {1, 2, 5, 15, 52, 226, 1201, 7851}

A267757 0 FC Number of terms of A072873 less than or equal to 10^n. {2, 5, 15, 52, 167, 517, 1547, 4493, 12706}